1) Use synthetic substitution
to find each value for P(x) = 4x3
- 3x2 +5.
a) P(-2)
b) P(3)
c) P(1/2)
d) P(-1/2)2) The leading coefficient
of a cubic polynomial is 2, and the coefficient of the linear term is -5.
If P(0) = 7 and P(2) = 21, find P(-1).3) Find the remainder when
x5 - 3x3 + x2 - 3 is divided by:
a) x - 1
b) x - 2
c) x + 1
d) x + 24) Find the remaining factors
for x4 - 10x3 + 35x2 - 50x + 24 if two
factors are x - 1, and x - 3.5) Sketch the graph of each
of the following equations. Note what happens at double and triple
roots.
a) y = (x - 1)(x + 3)(x - 2)
b) y = x2(x + 5)(x - 2)
c) y = (x - 1)3
d) y = x3(x - 1)26) There are 900 feet of
fencing available to enclose a rectangular plot with a fence down the middle
and parallel to two ends. What is the maximum area which can be enclosed?7) A bus line carries 2000
passengers per day at a rate of 20 cents per passenger. Management
wants to make a rate change, and they estimate they would lose 200 passengers
for every 5 cent increase. What rate should they charge to maximize
the revenue?